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June 2018 Estimating large correlation matrices for international migration
Jonathan J. Azose, Adrian E. Raftery
Ann. Appl. Stat. 12(2): 940-970 (June 2018). DOI: 10.1214/18-AOAS1175

Abstract

The United Nations is the major organization producing and regularly updating probabilistic population projections for all countries. International migration is a critical component of such projections, and between-country correlations are important for forecasts of regional aggregates. However, in the data we consider there are 200 countries and only 12 data points, each one corresponding to a five-year time period. Thus a $200\times200$ correlation matrix must be estimated on the basis of 12 data points. Using Pearson correlations produces many spurious correlations. We propose a maximum a posteriori estimator for the correlation matrix with an interpretable informative prior distribution. The prior serves to regularize the correlation matrix, shrinking a priori untrustworthy elements towards zero. Our estimated correlation structure improves projections of net migration for regional aggregates, producing narrower projections of migration for Africa as a whole and wider projections for Europe. A simulation study confirms that our estimator outperforms both the Pearson correlation matrix and a simple shrinkage estimator when estimating a sparse correlation matrix.

Citation

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Jonathan J. Azose. Adrian E. Raftery. "Estimating large correlation matrices for international migration." Ann. Appl. Stat. 12 (2) 940 - 970, June 2018. https://doi.org/10.1214/18-AOAS1175

Information

Received: 1 November 2017; Revised: 1 April 2018; Published: June 2018
First available in Project Euclid: 28 July 2018

zbMATH: 06980481
MathSciNet: MR3834291
Digital Object Identifier: 10.1214/18-AOAS1175

Keywords: Correlation estimation , high-dimension , international migration , maximum a posteriori estimation

Rights: Copyright © 2018 Institute of Mathematical Statistics

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Vol.12 • No. 2 • June 2018
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